Question 1207518: If 9 combination n : 8combination (n-2) = 9:4, find the values of n.
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
"cross multiply"
Rewrite using definition of C(n,r), and simplify
Rearrange factors so that each fraction has "similar" factorials
Simplify and solve
n = -8 or n = 5
Ignore the negative solution which makes no sense.
ANSWER: n=5
CHECK:
C(9,n)=C(9,5)=126
C(8,n-2)=C(8,3)=56
126/56=9/4
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Or, for a faster solution which gives you no practice with manipulating factorials....
n=3? C(9,3)=84; C(8,1)=8; 84/8 not = 9/4 No
n=4? C(9,4)=126; C(8,2)=28; 126/28 not = 9/4 No
n=5? C(9,5)=126; C(8,3)=56; 126/56 = 9/4 YES
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
The tutor greenestamps has a great solution. It's probably the method your teacher wants you to follow.
If your teacher allows you to use a spreadsheet then you can use the Combin function to find the answer very quickly.
Avoid the Choose function since that's something entirely different.
| n | A = Combin(9, n) | B = Combin(8, n-2) | A/B | Is A/B = 9/4 = 2.25? | | 2 | 36 | 1 | 36 | No | | 3 | 84 | 8 | 10.5 | No | | 4 | 126 | 28 | 4.5 | No | | 5 | 126 | 56 | 2.25 | Yes | | 6 | 84 | 70 | 1.2 | No | | 7 | 36 | 56 | 0.642857 (approx) | No | | 8 | 9 | 28 | 0.321429 (approx) | No | | 9 | 1 | 8 | 0.125 | No |
According to the table, n = 5 will turn "9 combination n" into 126 and "8 combination (n-2)" becomes 56.
126/56 = 9/4 = 2.25
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